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Knowledge Representation (Introduction)

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Knowledge Representation(Introduction)

Knowledge

Information

Data

Knowledge representation:

Information representation with support for inference

CSE 415 -- (c) S. Tanimoto, 2004 Knowledge Representation- Intro

Procedural vs Declarative

Knowledge can be operational:

“When you see a grizzly bear, run away fast!”

if Condition is true then do Action

e.g., production rules.

Knowledge can be declarative:

“A grizzly bear is a dangerous animal.”

predicate(object)

e.g., logical statements or relations

CSE 415 -- (c) S. Tanimoto, 2004 Knowledge Representation- Intro

Example of Declarative Representation: An “Isa” Hierarchy

Living-thing

Plant

Animal

Fish

Bird

Aquatic-bird

Land-bird

Great-blue-heron

CSE 415 -- (c) S. Tanimoto, 2004 Knowledge Representation- Intro

Inference with Isa Hierarchies Hierarchy

(A great-blue-heron is an aquatic-bird)

Isa(great-blue-heron, aquatic-bird).

(An aquatic-bird is a bird)

Isa(acquatic-bird, bird).

(Is a great-blue-heron a bird)

Isa(great-blue-heron, bird)?

“Isa” represents a relation which has certain properties that support types of inference.

CSE 415 -- (c) S. Tanimoto, 2004 Knowledge Representation- Intro

Binary Relations Hierarchy

A binary relation R over a domain D is a set of ordered pairs (x,y) where x and y are in D.

For example, we could have,

D = {a,b,c,d} R = {(a, b), (c, a), (d, a)}

If (x, y) is in R, then we write R(x, y) or x R y.

CSE 415 -- (c) S. Tanimoto, 2004 Knowledge Representation- Intro

Partial Orders Hierarchy

If for each x in D we have x R x, then R is reflexive.

If for each x in D and y in D we have

x R y and y R x imply x = y,

then R is antisymmetric.

If for each x in D, y in D, and z in D we have

x R y and y R z imply x R z,

then R is transitive.

If R has all 3 properties, R is a partial order.

CSE 415 -- (c) S. Tanimoto, 2004 Knowledge Representation- Intro

Examples of the Partial Order Properties Hierarchy

Isa is reflexive:

A bear is a bear.

-> Isa(bear, bear)

Isa is antisymmetric:

A bear is a wowie, and a wowie is a bear.

Therefore, bear and wowie represent the same things.

Isa(bear, wowie) & Isa(wowie, bear) -> bear = wowie

Isa is transitive:

A grizzly is a bear, and a bear is a mammal.

Therefore, a grizzly is a mammal.

Isa(grizzly, bear) & Isa(bear, mammal) -> Isa(grizzly, mammal)

CSE 415 -- (c) S. Tanimoto, 2004 Knowledge Representation- Intro

Redundant Facts Hierarchy

Any fact implied by others via the reflexive, antisymmetric, or transitive properties of a partial order can be considered redundant.

Suppose

a <= b

b <= c

c <= b

Then

a <= c is redundant.

a <= a is redundant.

b and c could be represented by one name.

CSE 415 -- (c) S. Tanimoto, 2004 Knowledge Representation- Intro

Inheritance of Properties via Isa Hierarchy

A fox is a mammal.

A mammal bears live young

Therefore a fox bears live young.

CSE 415 -- (c) S. Tanimoto, 2004 Knowledge Representation- Intro

Non-inheritance of Certain Properties Hierarchy

A neutron is an atomic particle.

There are three types of atomic particles.

Therefore there are three types of neutrons (??)

CSE 415 -- (c) S. Tanimoto, 2004 Knowledge Representation- Intro

Propositional Logic Hierarchy

The propositional calculus is a mathematical system for reasoning about the truth or falsity of statements.

The statements are made up from atomic statements using AND, OR, NOT, and their variations.

A more powerful representation system is the predicate calculus. It’s an extension of the propositional calculus.

CSE 415 -- (c) S. Tanimoto, 2004 Knowledge Representation- Intro

Propositional Logic Examples Hierarchy

P: a grizzly is a bear.

Q: a bear is a mammal.

R: a grizzly is a mammal.

P & Q -> R

Each proposition symbol represents an atomic statement.

Atomic statements can be combined with logical connectives to form compound statements.

~P, P & Q, P v Q, P = Q, P -> Q

CSE 415 -- (c) S. Tanimoto, 2004 Knowledge Representation- Intro

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